5 citations · 14 across the 15 of their papers we have counts for
9 papers · 1 filter
Continued Fraction approach to Gauss Reduction Theory
Oleg Karpenkov
Jordan Normal Forms serve as excellent representatives of conjugacy classes of matrices over closed fields. Once we knows normal forms, we can compute functions of matrices, their…
On a periodic Jacobi-Perron type algorithm
Oleg Karpenkov
In this paper we introduce a new modification of the Jacobi-Perron algorithm in three dimensional case and prove its periodicity for the case of totally-real conjugate cubic vector…
On Hermite's problem, Jacobi-Perron type algorithms, and Dirichlet groups
Oleg Karpenkov
In 1848 Ch.~Hermite asked if there exists some way to write cubic irrationalities periodically. A little later in order to approach the problem C.G.J.~Jacobi and O.~Perron generali…
Generalised Markov numbers
Oleg Karpenkov, Matty van-Son
In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particul…
Open problems in geometry of continued fractions
Oleg Karpenkov
In this small paper we bring together various open problems on geometric multidimensional continued fractions.
Rational approximation of the maximal commutative subgroups of GL(n,R)
O. Karpenkov, A. Vershik
How to find "best rational approximations" of maximal commutative subgroups of GL(n,R)? In this paper we pose and make first steps in the study of this problem. It contains both cl…